Let `A B C` be a triangle of area 24sq. units and `P Q R` be the triangle formed by the mid-points of sides of ` A B Cdot` Then the area of ` P Q R` is 12 sq. units (b) 6 sq. units 4 sq. units (d) 3 sq. units

Explanation

Given that area of `triangleABC=24` square units

`therefore` Q and R mid-points of AB and AC.

By mid-point theorem

`RQ|\|BC` and `RQ=1/2BC`

Similarly, `PQ|\|AB` and `PQ=1/2AB`

Now, `RP|\|AC` and `RP=1/2AC`

`therefore` area of `trianglePQR`=`1/4` area of `triangleABC`

=`1/4xx24`=`6` sq. units

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